
1.1 Modelling of Heat flow during Welding using ANSYS
1.1.1 Introduction
The steady state heat conduction in a moving solid can be described by the following
equation:
α∇
2
T − ⅆ
δT
δx
= 0
Solution of the above equation gives the following expressions for the temperature field
round a "quasi-stationary" heat source. This steady-state assumption was first used by
Rosenthal to simplify the mathematical treatment of heat flow during welding. [1]
Rosenthal’s Two-Dimensional Equation
Rosenthal used the following simplifying assumptions to derive analytical equations for heat
flow during welding:
1. steady-state heat flow
2. point heat source
3. negligible heat of fusion
4. constant thermal properties
5. no heat losses from the workpiece surface
6. no convection in the weld pool
Figure 1: Coordinate system (x, y, and z) moving with heat source. From Sindo Kou